Continuity & Bernoulli worksheet with answers

Free printable Continuity & Bernoulli worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
12d1​ = 150 mm, v1​ = 2.25 m/sd2​ = 75 mm, v2​ = ?

Water flows through a pipe that narrows from 150 mm to 75 mm in diameter. The velocity in the wide section is 2.25 m/s. Find the velocity v2 in the narrow section.

d1 = 150 mmd2 = 75 mmv1 = 2.25 m/s
v2 = m/s
2.Easy
12d1​ = 100 mm, v1​ = 1 m/sd2​ = 40 mm, v2​ = ?

Water flows through a pipe that narrows from 100 mm to 40 mm in diameter. The velocity in the wide section is 1 m/s. Find the velocity v2 in the narrow section.

d1 = 100 mmd2 = 40 mmv1 = 1 m/s
v2 = m/s
3.Medium
d1​ = 80 mmd2​ = 40 mm12p1​ − p2​ = 46 kPaQ = ?

Water flows through a horizontal venturi meter with an inlet diameter of 80 mm and a throat diameter of 40 mm. The pressure at the inlet is 46 kPa higher than at the throat. Ignoring losses, find the flow rate Q.

d1 = 80 mmd2 = 40 mmp1 − p2 = 46 kPaρ = 1000 kg/m³
Q = L/s
4.Medium
12d1​ = 100 mm, p1​ = ?d2​ = 75 mm, p2​ = 90 kPa

Water flows at 24 L/s through a horizontal pipe that narrows from 100 mm to 75 mm. The pressure in the narrow section is 90 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 24 L/sd1 = 100 mmd2 = 75 mmp2 = 90 kPaρ = 1000 kg/m³
p1 = kPa
5.Hard
12d1​ = 200 mm, p1​ = 370 kPad2​ = 100 mm, p2​ = ?Δz = 7 m

Water flows up through a pipe that narrows from 200 mm to 100 mm while rising 7 m. At section 1 the pressure is 370 kPa and the velocity is 3 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 200 mmd2 = 100 mmp1 = 370 kPav1 = 3 m/sΔz = 7 mρ = 1000 kg/m³
p2 = kPa
6.Hard
12d1​ = 75 mm, p1​ = 180 kPad2​ = 50 mm, p2​ = ?Δz = 8 m

Water flows up through a pipe that narrows from 75 mm to 50 mm while rising 8 m. At section 1 the pressure is 180 kPa and the velocity is 3 m/s. Ignoring losses, find the pressure p2 at section 2.

d1 = 75 mmd2 = 50 mmp1 = 180 kPav1 = 3 m/sΔz = 8 mρ = 1000 kg/m³
p2 = kPa

Answer key

  1. 1. v2 = 9 m/s
  2. 2. v2 = 6.25 m/s
  3. 3. Q = 12.45 L/s
  4. 4. p1 = 100.1 kPa
  5. 5. p2 = 233.8 kPa
  6. 6. p2 = 83.24 kPa

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